Hameed et al. Iraqi Journal of Science, 2020, Vol. 61, No. 4, pp: 845-853 DOI: 10.24996/ijs.2020.61.4.18 ____________________________ *Email: bbsmh896@gmail.com 548 On the Estimation of (    ) in Cased Inverted Kumaraswamy Distribution Bsma Abdul Hameed*, Abbas N. Salman, Bayda Atiya Kalaf Department of Mathematics, College of Education for Pure Sciences, Ibn Al – Haitham, University of Baghdad Iraq, Baghdad, Iraq Received: 16/7/ 2019 Accepted: 21/9/2019 Abstract This paper deals with the estimation of the stressـstrength reliability for a component which has a strength that is independent on opposite lower and upper bound stresses, when the stresses and strength follow Inverse Kumaraswamy Distribution. D estimation approaches were applied, namely the maximum likelihood, moment, and shrinkage methods. Monte Carlo simulation experiments were performed to compare the estimation methods based on the mean squared error criteria. Keywords: Inverted Kumaraswamy distribution, Stress ـStrength reliability, Maximum likelihood estimator, Moment estimator, Shrinkage estimator حول تقدير(    ) في حالة توزيعرا سوامي كوما المعكوس مه عبد الحميد بد * داء عطيه خلف سلمان, بي , عباس نجم اضيات, كمية قدم الري التربيةهم لمعم الصرفة اقمعة بغجاد, العرلهيثم, جا , ابن ا خلصة ال يتعم ق مهضهع البحث ب تقجيرلجهاد معهلية ا- لمتانة احتهي لنظام ي لجيها متانة واحجةى مركبة عم تعرض الى وتجهاد اسفلن العمى وال محجد م و يتبعاندتقمينتانة مد والملجهاة كل من ا في حال تهزيع ا سهامي كهمار ائق بأستخجام طر المعكهسختمفة تقجير م منهان العظم,لمكا ا مقجر العزوم و ات مقجر التقمص. خجمت طريقة است مح ا كاة مهنت ي كارله لمقارنة م بين طر ائ التقجير الم ق دتخجمة ب العتماد عمى معيار متهسط ت الخطأ. مربعا 1. Introduction The stress-strength model in the reliability research describes the life of a component which has a random strength X and is subjected to a random stress Y. This problem arises in the classical stress– strength reliability where one is interested in estimating the proportion of the times the random strength X of a component exceeds the random stress Y to which the component is subjected [1]. An important case is the estimation of R = P(    ) which represents the situation where the strength X should not only be greater than stress   but also be smaller than stress  . Because of that, modern engineering systems may have more than two components [2]. For instance, many electronic components cannot work at very high or very low voltages. Similarly, person's blood pressure should lie within two limits, i.e., systolic and diastolic. The stress- strength model of P(    ) was studied in many branches of science, such as psychology, medicine, pedagogy, etc.[3]. ISSN: 0067-2904